Outputs (2)

Universality of critical behaviour in a class of recurrent random walks (2004)
Journal Article
Hryniv, O., & Velenik, Y. (2004). Universality of critical behaviour in a class of recurrent random walks. Probability Theory and Related Fields, 130(2), 222-258. https://doi.org/10.1007/s00440-004-0353-z

Self-avoiding polygons: sharp asymptotics of canonical partition functions under the fixed area constraint (2004)
Journal Article
Hryniv, O., & Ioffe, D. (2004). Self-avoiding polygons: sharp asymptotics of canonical partition functions under the fixed area constraint. Markov processes and related fields, 10(1), 1-64

The paper considers the ensemble of self-avoiding paths in $Z^2$ which join the positive vertical axis with the positive horizontal axis, and take value on the first quadrant of the plane. To each such path $\omega$ is associated its length $|\omega|... Read More about Self-avoiding polygons: sharp asymptotics of canonical partition functions under the fixed area constraint.